一类有理参数三次曲线的形状分析(英文)

一条有理参数三次 H-样条曲线是由一组控制顶点和两顶点连线上的百分比参数所确定。移动一个顶点仅影响三段曲线。有理 H-样条具有许多类似于 B-样条曲线的性质 ,也有 B-样条不具有的性质。本文是在文 1 ]基础上的继续和发展 ,主要对有理 H-样条曲线的形状进行分析 ,讨论其诸如拐点和奇点的几何特征 ,给出有理参数平面三次 H-样条曲线在非退化情况下有拐点的充要条件 ,并证明在区间 ( 0 ,1 )内曲线段无奇点的结论。为了便于对参数曲线段的形状控制和几何特征的进一步认识 ,在许多的实际应用中 ,需要分析参数曲线段上有无多余拐点和奇点 ,如果有就要消除它。故本文的研究结果无论对理论或实际应用都非常重要。

SHAPE ANALYSIS FOR A KIND OF RATIONAL PARAMETRIC CUBIC CURVES

A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects three curve segments. This paper is the succession and development of reference of Tang Yuehong. We analyze the geometric features like cusps and inflection points in the curve and calculate the cusps and inflection points, then give a necessary and sufficient condition to the inflection points in the curve when it is non degenerative, and finally show that the curves have no cusps in the interval (0,1). In many applications, it is desirable to analyze the parametric curves for undesirable features like cusps and inflection points